Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | Dic7×M32 |
| Sylow | C7 ⋊ C4×M32 |
196 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | Dic7×#347, #13268625, #13268803, … |
| maximal normal subgroup of | Dic7×#347, #13268625, #13268803, … |
| maximal quotient of | M32×C7⋊C8, #13262790, #13262820, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3938);